quadratic equation solving mistake

You have not made any mistake.

The final equation you have obtained is $$17x^2-3x-14=0$$ $$17x^2-17x+14x-14=0$$ $$17x(x-1)+14(x-1)=0$$ $$(17x+14)(x-1)=0$$ which has the roots $1$ and $\frac{-14}{17}$.


Your working is all fine. Only the last step was remaining to be written down after factoring.

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Algebra Precalculus

Quadratics

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